It's worse than that, Martze, given that the enemies don't turn around instantaneously, so instead of a distance of 16 squares we should be counting 16+x, for some x which I don't know.

Watching the shortest two columns until they line up again, unless I miscounted, took 38 periods of the smallest one to realign with 34 periods of the second-shortest. So it appears x=1 and we really have lcm(17,19,21,23,25) = 3900225 (those are relatively prime) squares / the enemy speed.

ETA: and it looks like you've omitted a factor of 2 corresponding to having to go up and down, so it's really 7800450 squares / the enemy speed, which is just short of 5 days 16 hours if it is 16 squares / second.

ETA 2: though maybe it's still possible to make it through if some of the columns are one square off from their starting position. I don't feel like Chinese remainder theoreming that up now...